An Open Letter

Professor Simon Tavare
President, The London Mathematical Society
57-58 Russell Square
London  WC1B 4HS

Dear Professor Tavare,

I am writing to express my concern at the recent announcement by LMS of the
planned closure of the LMS Journal of Computation and Mathematics (JCM).

First let me indicate why I have an interest in this issue.  My main research field is Computational Algebra (CA). For the past 25 years I have headed the Computational Algebra Group at the University of Sydney which typically comprises 8–15 full-time researchers. The long-term goal of the group is to develop effective algorithms for solving key computational problems in a range of areas of mathematics, with particular emphasis on algebraic geometry, group theory and number theory. Hence, we need ready access to existing work in the various fields of interest and we also need suitable journals to publish an average of 20 papers per year. The researchers in the group need to develop their careers by publishing in journals with a good reputation. Over a long period I have been involved in initiatives to establish suitable journals for this new field. In particular, I was a member of a small group that persuaded Academic Press to create the Journal of Symbolic Computation in 1985 and was one of the initial associate editors. However, I should state that I have never had any connection with JCM.

Computational Algebra, as a recognised research topic in mathematics, did not exist  before  1970. Beginning  around  1970, researchers discovered  completely new algorithms that are much faster than classical algorithms for calculations such as computing the GCD of two polynomials over Z or factorising a polynomial  over Z. During  the  1970’s  and  1980’s  it  gradually  became  clear  that alongside the theoretical content of most branches of mathematics, there also exists a rich body of algorithms.  This is particularly evident in the case of finite groups.  By the late 1990’s computational methods were increasingly used in developing theory. We have now reached the stage where tens of thousands of published mathematical papers dealing with theory cite some use of  computational techniques in producing their results. As an example, a simple web search turned up some 5000 papers published up until 2013 citing the Magma Computer Algebra system alone. Also, computational methods make possible the application of many ideas from theoretical pure mathematics to applied problems. An example of this is the use of elliptic curves in cryptography.

It is natural to assume that theoretical papers using standard computational tools would be published in the usual theoretical journals and this is what generally happens.  Some CA papers also appear in theoretical journals but this can be unsatisfactory for several reasons.  Firstly, the criteria used to assess a theoretical paper can be different to those employed for papers that are contributions to CA methods.  Secondly, the development of the field of CA is greatly enhanced by having CA papers appear in specialised journals in that it allows people to quickly find papers of interest.

A small number of journals specialising in CA or more generally in computational mathematics (CM) have been created.  The most important of these are the Journal of Symbolic Computation,  Experimental Mathematics and JCM. In addition, Mathematics of Computation (Math Comp) and the Journal of Algebra each have sections for CA/CM type papers.  The non-numerical section of Math Comp tends to be dominated by number theory papers and it is not seen as a suitable place to publish papers in areas of CA other than number theory.

In the beginning, CA algorithms tended to be based on fairly elementary theory but in recent years it has been found that deep theoretical ideas can be a basis for constructing very powerful algorithms.  Examples include the development of n-descent  to  find  rational  points  on  curves  having  low  genus,  the  use  of the  classification  theorem  for  finite  simple  groups  (CTFSG)  as  the  basis  for algorithms for finite groups, and computing properties of schemes using coherent sheaves. In  the  1960’s  and  1970’s  A was seen  as  having  close  links  with computer science and many of the people involved in setting up JSC were on the CS side of the fence. While it does publish many papers that are concerned with algorithms based on deep mathematical ideas, JSC still has a strong CS orientation. The attraction of JCM is that it is at the mathematical end of the spectrum. It makes possible the publication of papers having deep mathematical content appear in a journal run by  one of the  world’s  premier  mathematical societies. Authors accepted for publication in JCM can be confident that their paper will have credibility within the mathematical community.

The computational mathematics field is very active and now produces hundreds of papers every year.  It has taken a number of years to reach the point at which a respectable number of good papers were being submitted to JCM. A journal in a new area  takes  time  to  be  accepted  and  if  it  were  to  be  continued  one would expect it to become the journal of choice for good papers dealing with computational methods specific to a number of active research areas in (pure) mathematics. At present it attracts many strong papers in computational group theory and computational number theory but less in commutative algebra and algebraic  geometry.  It  should  be  possible  to  remedy  this  without  too  much effort. The creation of JCM was a vote of confidence in the value and importance of computational mathematics and I fear that its closure will turn that into a vote of no confidence at a time when we are struggling to attract enough good graduate students into the area.

The suggestion that JCM be replaced by another journal makes little sense as it will then take the new journal 10–15 years before it attracts sufficient good papers. Having closed one computational journal, prospective authors are likely to be very nervous about committing papers to a new LMS computational journal. It would be far better to revise the mission of JCM and continue to build on the existing author base.

I should point out that while it is not unknown for a journal to close, it is
a serious matter to close a journal that is one of the few that specialise in a
growing field such as computational mathematics. This will certainly impact
the field in a negative way. Among other things, it damages the standing of
papers that have been published in the journal.

In closing I mention a particularly valuable aspect of JCM. In March 2015, Jean-Pierre Serre gave a lecture at Harvard in which he expressed concern about some aspects of the effort that produced the CTFSG. A particular criticism was that many recent results in mathematics rely on the character tables that appear in Atlas of Finite Groups but there are no proofs of correctness for these tables. Each table was produced character-by-character by a mathematician who may have used a computer for performing arithmetic with the so-far known characters. An algorithm for computing character tables developed by my colleague Bill Unger in 2004 offered another approach. This algorithm takes as input, permutation or matrix generators for a group and applies a theorem of Brauer to induce the characters from elementary subgroups. The whole process is completely automatic. So Unger and I have now computed most of the Atlas character tables using this method (BM and M are the only groups the method cant handle). We found that generally they agree with the Atlas tables as stored in the GAP package. At this point we want to publicise this work and use it to start a debate about the level of confidence mathematicians expect for results produced by computer. It would seem that JCM would have been the ideal forum for such an important discussion.

To summarise, research in computational mathematics (in the sense of exact
computation) has led to the discovery of many amazing algorithms which in some cases open up areas of theoretical mathematics to further development (L-functions and the Langlands conjectures, for example). A satisfactory set of journals for the publication of non-numerical computational mathematics has yet to emerge. JCM is one of a handful of journals with the right pedigree and right editorial policies which makes it a journal that we badly need for the continued development of computational mathematics.

I hope that some way can be found to continue the publication of this journal.

Yours faithfully,

John Cannon
Computational Algebra Group
The University of Sydney
NSW 2006 Australia

Posted by: Administrator | 25/01/2016

Professor Alexandre Borovik, University of Manchester

I have never published anything in the JCM and had never been involved
in its publication and therefore have no personal interest in its existence.

I wish to say a few words about the scope of the JCM. It seems to me
that Terry Lyons’ criticism of the Journal is based on an arbitrary
assumption that the Journal should publish quality papers from so-called
“experimental” mathematics and from numerical mathematics. But the JCM
is unlikely to be competitive in these areas are because there is plenty
of journals around already covering them.

But the JCM plays, and is in position to continue to play, a unique role
as the leading journal in specific, increasingly important,
cross section of pure mathematics: symbolic and/or absolute precision
arithmetic computations, frequently at the limits of capacity of modern
computers, in algebra, representation theory, combinatorics, number
theory, algebraic geometry, etc. The role of mathematical work of this
type will only increase in future.

Let us take look at a very recent paper which I picked on the very first
page of the JCM site hosted by CUP because the subject appeared familiar
to me:

John Ballantyne, Chris Bates and Peter Rowley, The maximal subgroups of
E_7(2), LMS J. Comput. Math. 18 (1) (2015) 323-371.

A few general words about the area : finite groups appear in mathematics as automorphism groups of mathematical structures. In particular, they act on sets. The so-called primitive actions are building blocks of actions of finite groups on sets. The so-called simple groups are building blocks of groups. To make Classification of Finite Simple Groups, one of the key results of 20th century, fully usable across mathematics, one needs to know primitive permutation representation representations of simple groups. It is an elementary fact that description of primitive permutation representations of a finite group is equivalent to description of maximal subgroups in the group. E_7(2) is one of finite simple groups; it is big, it contains contains about 10^40 elements. It is a very big haystack to search for the proverbial needle; 10^40 straws have the same mass as 1 million Suns. In the paper, a much more difficult problem is solved: in a haystack of that size, specific symmetric configurations of straws  are identified, and fully described.

And now is my assessment of the paper:

  1. The result may appear to be narrow and specific, but it will stay
    relevant for decades to come, because it is about a concrete, eternal,
    and important mathematical object.
  2. Methods are an intricate intertwining of subtle and difficult mathematics with hard but subtle computations.
  3. It is hard to find any other journal to publish this paper together with 51 MB (3.36 MB in compressed form) of electronic files supporting the calculations.
  4. Two younger authors of the paper  are brilliant young mathematicians with proven ability to compute in areas where no mathematician has computed before. In my opinion, this makes them pretty special,  As it has already been said in this discussion about similar situations, peer-reviewed publication of their papers is crucially important for the future career of young mathematicians.

This small case study explains, I think, why the JCM is a unique and special journal and why closing it is not in the interests of mathematics  and, in my humble opinion, not in the interests of the nation.

To conclude, a comment from Rob Wilson (placed here with his kind permission):

I am perhaps at the opposite extreme, having published ten papers in the
JCM over the past 14 years, with another one in press at the moment.
Some might say this is a ‘conflict of interest’ that disqualifies me
from speaking, but I fully endorse what Sasha has said about the type of
computation and mathematics that is represented in the JCM. It is a much
misunderstood and even despised area of mathematics, but in fact is hard
core computation on the edge of the impossible.

Posted by: Administrator | 24/01/2016

Professor Derek Holt, Editor of the JCM: Costs of the JCM

There has been some uncertainty about the exact nature of the direct costs
of the JCM that have been obtained from official LMS Annual Reports filed with
the Charity Commission in 2005 — 2015:

£ 467 in 2005
£ 741 in 2006
£ 367 in 2007 (11 months)
£ 341 in 2008
—— in 2009 (no figure given)
£ 4,294 in 2010
£ 4,894 in 2011
£ 5,930 in 2012
£ 6,180 in 2013
£ 7,224 in 2014
£ 15,275 in 2015

I have finally been able to account for these figures myself, or at least those
from 2010 onwards.

The exact figures are confidential, but from 2010 the LMS has been paying CUP
a fixed annual fee for hosting the journal, together with an extra cost for
each published paper, which does not depend on the length of the paper. These
charges rise with inflation each year. In addition, the LMS pays another
organisation a price per published page for typesetting and copy-editing.
There are currently no additional charges for supplementary material
accompanying published papers. I have done some calculations, and these charges
account more or less exactly for the figures quoted for 2014 and 2015.

The steady increase from 2010 onwards was mainly due to the increasing number
of published papers and pages, which was a result of the editors achieving one
of the targets set to them by the Publications Committee in 2012.

The large increase in 2015 was mainly due to the journal publishing the ANTS 14
conference proceedings. The LMS did receive some payment for this from the
conference, but they decided to keep it cheap that time, so they did not
charge enough to cover the direct costs. For the 2016 ANTS proceedings, they
will be charging significantly more, and they expect to make a profit at least
on the direct costs.

Posted by: Administrator | 23/01/2016

Professor Dr Volker Mehrmann, TU Berlin.

A colleague pointed out the plan to close the LMS J. of Computation and Mathematics to me. With the danger of repeating other peoples arguments, I would like to suggest that mathematical societies like LMS should rethink the issue of closing green open access journals but rather put an effort and further funds into more such journals. I am not commenting on this particular journal but suggest that in general more green open access is generated by societies to replace a number commercial journals (of all publishers). I don’t believe we can replace all commercial journals by open access butI think it is time that the communities make this effort to ensure the furture of science and the free access to information. Scientific societies (who else) act in the interest of their members and should therefore invest some of their funds into such activities.

A colleague wrote to me:

Executive Secretary  writes

“3.  An option has been added to the Form to allow members to grant the appointed proxy the option to vote at the proxy’s discretion.”

but this is not on the form she sent

My own attempts to open the file  SGM_2016_02_05_Proxy_Voting_Form_UPDATED.docx attached to Executive Secretary’s email of 21 January 2016  by some standard Microsoft software led to  results like this:Proxy Voting Form

and this:

Proxy_Voting_Form_UPDATED_22Jan16

As you can see, all 3 options mentioned in the document have disappeared. Using my arsenal of text editors, I was able to recover some meaningful text. But I  still do not know whether I have recovered the text in full. It also appears that some members managed to recover only two declared options out of three.

I am aware now, from correspondence with my colleagues, that the problem persists and affects other members of the Society. In my opinion, it has to be immediately fixed for the vote to be valid.

In my opinion, it is not advisable to circulate the LMS voting documents in a format which is not compatible with software widely used by the members of the LMS.

Posted by: Administrator | 22/01/2016

Professor John Voigt, Dartmouth College

I would also like to write in support.

In my opinion, the LMS Journal of Computation and Mathematics plays a crucial role in the dissemination of influential papers in computational algebra and number theory. There are unfortunately few mathematics journals that publish papers in computation (in pure mathematics): there is the highly regarded Mathematics of Computation, published by the AMS (with an enormous backlog), and Journal of Symbolic Computation, published by Elsevier–and then an enormous gap. (I choose not to publish in Elsevier journals for reason of publishing practices, so only Math. Comp. is available.) Too many other journals turn away computational papers, either because the journal is domain-specific and therefore not tailored for computation, or because the journal is for a general audience and unwilling to publish “too many” computational papers. I have sent some of my best computational work to LMS JCM and had planned to continue to do so, and I have encouraged my colleagues to do so as well. I could see the reputation of this journal grow within our community over the past few years, filling a niche that will only grow in importance in the years ahead. Its cancellation will have a significant negative impact.

Posted by: Administrator | 20/01/2016

Professor Gavin Brown, Warwick University

I write in support of the JCM.

I am conscious that I do not know the full ins and outs of the LMS’s decision to close JCM. My understanding is that the LMS is considering and developing ideas in which they can continue to support dissemination of computationally-supported mathematics, which is, after all, a central plank of contemporary maths.

I can imagine there are better ways of spending LMS resources on this, but until I have some idea of what they are likely to be I continue to support JCM. (The resources do not seem so vast in any case.)

I note that personally as an editorial advisor the majority of submission I see are rejected by referees, and I only recommend accepting those that the referees deem of real scientific value. So although the journal’s impact factor is not high, I don’t think we should interpret that as saying that the value of the journal to science is not high.

It’s worth me saying that I am not against closing the journal if there is a better suggestion on the table – I am not being conservative for the sake of it. But I would like to see the better suggestion first. If the LMS truly does hope to use its resources more wisely in this direction, I would suggest keeping JCM going for 2 or 3 more years until we have more concrete suggestions to compare it against. If the JCM is rendered obsolete by a better service to computational (pure) maths, then it could close then, with a relatively small sum having been invested in keeping it alive as a safety net.

I would rather that the LMS be over-represented in its dissemination of computational maths for a couple of ‘overlap’ years than that it be not represented at all.

I have been  Editor In Chief of the JCM since 2008, and so I am in a good position to assess its overall quality, and whether that has changed over the period. Of course, I am not a disinterested assessor, and I hope very much that the decision to close the JCM will be reversed.

On balance, I think that the quality has remained at at about the same level since 2008. All papers are refereed, and the three journal editors come to a decision taking into account the referees’ reports and the assessments of the Editorial Adviser who handled the paper. (So it is only the three editors who can accept a paper.) We generally impose high standards, and only accept papers that have positive reports. I am also on the editorial board of the computational section of the Journal of Algebra (which has an impact factor of 0.599) and, in my opinion, the typical standard of JCM papers is roughly the same as that of typical computational Journal of Algebra papers.

It could be certainly be argued that the mathematical quality of papers published by the main LMS journals (Proceedings, Journal, Bulletin of LMS) is generally higher than that of JCM papers, and I would not dispute that. But the JCM is catering for a different type of paper. For example, it publishes details of new and innovative software packages, and it provides a permanent record of the details of lengthy computations, which enables them to be repeated and and verified independently if necessary. Such results frequently form essential components of significant large-scale research projects in fundamental areas of mathematics, such as determining the properties of the finite simple groups, and establishing results on elliptic curves.

In 2012, when the question of the possible demise of the JCM was first raised, the editors were assigned a number of targets. Specifically we were asked to increase the total number of papers published without a decrease in quality, and to publish at least two conference proceedings during the following three years. In the event, we only published one conference proceedings (ANTS 14), but the JCM will publish the ANTS proceedings again in 2016.

I would argue strongly that we achieved the first of these aims (the total page count went up from 423 in 2013 to 773 in 2015).  Since I have been involved in the acceptance of all papers published during this period, I can testify that we have maintained the same rigorous standards throughout.

I have recently looked again at the 33 papers published by the JCM in 2015, and at the referee reports and ensuing discussions. I was immediately impressed (and to some extent surprised) by the broad range of topics covered by these papers. This broadening of subject area has been the result of a number of new Editorial Adviser appointments over the past few years. As well as many papers in the traditional areas covered by the JCM – (i.e. Discrete Mathematics, such as Group Theory, Representation Theory, Lie Algebras, Number Theory, Geometry) – there are at least five papers concerned with numerical computation, and solving differential equations. It seems particularly unfortunate that the journal has been closed at a time when the recent expansion of the editorial board is starting to bear fruit.

Of these 33 papers, I would rate about 25 of them as strong and acceptable for publication in any good quality journal in this area (such as the computational section of the Journal of Algebra). Of the others, about four were borderline, and could have been rejected. If the JCM is allowed to continue then I would be in favour of being slightly more selective in future and being less inclined to give borderline papers the benefit of the doubt.

I have to be cautious about quoting from referees’ reports, but comments on some of the stronger papers included: “a new and important result”, “a critical step in the [research project concerned]”, “a major paper with new ideas about an important computational problem”, “a result that will have a strong impact in the field”.

Added later: In the information circulated to LMS members in advance of the Special General Meeting, Paper D, “A paper by the LMS Publications Secretary”, Paragraph 3, it states:

 The minimum targets set centred around the quality and quantity of papers   published, and the commissioning of two good quality conference   proceedings, where the editors believed there was scope to develop the   journal. Publications committee met in early 2015 to consider progress; it   was clear that the targets had not been met, and it was a moot point as to   how much progress had been made towards them.

I believe that this statement is highly misleading. On the contrary, it was not at all clear that the targets had not been met, and it was completely clear how much progress had been made towards them. We were asked to increase the number of published papers and pages by a specified amount without decreasing quality – we were not asked to improve the quality. In the event,
we exceeded the the requested increases in quantity while maintaining quality. It is true that we only published one set of conference proceedings in the period 2012 – 2015, but we will be publishing another in 2016. So I would say rather that we were failed on a technicality.

Derek Holt, 16/1/16.

Posted by: Administrator | 14/01/2016

Professor Dr. Gerhard Hiss, RWTH Aachen University

With considerable consternation I have learned that the Council of  the London Mathematical Society decided to close down its Journal of Computational Mathematics.

Ever since its launch in 1998, I have considered the LMS JCM as  a truly innovative and valuable journal.

It is innovative not only as one of the first online journals of its time, but also by making full use of this publishing medium, for example by offering the possibility to attach large tables of data to an article.

It is valuable since it fills a real demand in the community of mathematicians whose work involves, possibly to rather different degrees, experimental, constructive and algorithmic aspects.

(By the way, I consider the approach to Mathematics using computers, for example to perform a large number of experiments, or to produce discoveries which are otherwise out of reach, usually not just by running an algorithm but in an interactive manner, rather forward-looking.)

As the managing editor of the Computational Section of the Journal of Algebra, I do appreciate the need of journals with a focus on computational mathematics.

The LMS JCM is presumably the best journal to date satisfying this need, and it does cover all areas of mathematics, so that I really cannot follow the LMS Council’s decision to close their JCM down.

In my view it is very unfortunate that the Council of the LMS has
closed down the Journal of Computation and Mathematics.

The Journal of Computation and Mathematics has been a journal of
excellent quality and very high international reputation. It had a
wide range of very well known authors.

The fact that it allows to publish papers together with relevant
programming code was unique. I believe that this was an extremely
valuable feature of this journal.

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